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Probability question. Please help?
I solved this question my way and then looked at the answers and my answer was wrong. Please explain to me why. Here's the question:
Each packet of Cruncho cereal contains one free fridge magnet. There are five different types of fridge magnet to collect. They are distributed, with equal probability, randomly and independently in the packets. Keith is about to start collecting these fridge magnets. Find the Probability that Keith collects all 5 types of fridge magnets by buying just 5 packets.
My (wrong) answer:
5C5 * (1/5)^5 = 0.000 32
which makes sense to me because (1/5) is the probability of getting each fridge magnet. Raising that to the power of 5 gives the probability of getting 5 magnets. Then multiply by 5 to get the number of possible ways of doing this.
The actual answer:
1*(4/5)*(3/5)*(2/5)*(1/5) = 0.0384
But how does that make sense? the question says probabilities are independent!
Please please help!
2 Answers
- 9 years agoFavorite Answer
Okay, say the different types of magnets are 'a', 'b', 'c', 'd' and 'e'.
Probability of getting one of them in the first buy is 100% =1;
Now there are 4/5 left; If another one, say 'b' is taken this time then 3/5, then 2/5, then 1/5.
Therefore total probability changes because options reduce, hence answer is = 1*4/5*3/5*2/5*1/5;
- cidyahLv 79 years ago
In your answer "Then multiply by 1 to get the number of possible ways of doing this."
5C5 = 1
Anyway, your answer is .000 32 is done correctly. That is, you have multiplied by 1 (not 5).
This is the argument for the actual answer.
The first time, it doesn't matter what type he collects. The second time, his collection should not include the first collection and from the remaining 4, it doesn't matter what he collects. The probability of this happening is 4/5. The third time, he should not collect what he collected the first and the second time and from the remaining 3, he has a probability of 3/5 and so on.
